In this chapter, we illustrate R to fit some common regression models from a Bayesian perspective. We first outline the Bayesian normal regression model and describe algorithms to simulate from the joint distribution of regression parameters and error variance and the predictive distribution of future observations. One can judge the adequacy of the fitted model using the posterior predictive distribution and the inspection of the posterior distributions of Bayesian residuals. We then illustrate the R Bayesian computations in an example where one is interested in explaining the variation of extinction times of birds in terms of their nesting behavior, their size, and their migratory status. Zellner (1986) proposed a simple way of inputting prior information in a regression model. We illustrate the use of Zellner’s class of g priors to select among a set of best regression models. We conclude by illustrating the Bayesian fitting of a survival regression model.
KeywordsPosterior Distribution Predictive Distribution Extinction Time Inverse Gamma Predictive Density
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